TAUNTON — Police Chief Edward Walsh says responding to reports of heroin overdoses is “a constant drain,” not only on his department, but on local ambulance company American Medical Response and the city’s fire department, which is required to respond to medical emergencies.

Walsh noted the obvious paradox that even though word has gotten out during the past couple of months about the rising number of heroin overdoses — seven dead so far this year out of a total of nearly 90 overdoses — it’s done nothing to stem the tide.

“It seems once they hear about how strong it is they want to try it for themselves,” he said.

Those who survive a heroin overdose usually do so because of emergency responders who administer the prescription antidote Narcan, which comes both in a nasal spray and in an injection form.

Many of the overdoses in the city, police said, can be attributed to cheap heroin being cut, or laced with, the powerful and potentially lethal painkiller fentanyl.

Kate Brauneis, clinic director of Taunton’s Habit OPCO methadone and suboxone treatment center, said the spike in heroin overdoses has had a negligible effect in terms of people seeking help.

“You would expect there to be a spike, but there really hasn’t been,” she said.

Brauneis said the downtown Taunton clinic serves about 340 people with addiction problems.

Habit OPCO, which has 22 treatment centers in New England, New Jersey and Pennsylvania, was purchased by California-based CRC Health Group, the nation’s largest addiction-treatment provider, in December.

Walsh said his department and other local law enforcement departments and agencies, including the U.S. Drug Enforcement Administration, will keep the pressure on drug dealers.

Taunton police detectives, with the aid of DEA agents and detectives from Easton, Norton and Raynham, arrested five people early Friday morning on cocaine and heroin charges. One of those arrested on trafficking charges allegedly had 140 grams of cocaine and 36 grams of heroin when he was apprehended.